#ifndef STAN_MCMC_HMC_NUTS_BASE_NUTS_HPP
#define STAN_MCMC_HMC_NUTS_BASE_NUTS_HPP

#include <stan/interface_callbacks/writer/base_writer.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <stan/mcmc/hmc/base_hmc.hpp>
#include <stan/mcmc/hmc/hamiltonians/ps_point.hpp>
#include <algorithm>
#include <cmath>
#include <limits>
#include <string>
#include <vector>

namespace stan {
  namespace mcmc {

    struct nuts_util {
      // Constants through each recursion
      double log_u;
      double H0;
      int sign;

      // Aggregators through each recursion
      int n_tree;
      double sum_prob;
      bool criterion;
    };

    // The No-U-Turn Sampler (NUTS) with the
    // original slice sampler implementation
    template <class Model, template<class, class> class Hamiltonian,
              template<class> class Integrator, class BaseRNG>
    class base_nuts_classic:
      public base_hmc<Model, Hamiltonian, Integrator, BaseRNG> {
    public:
      base_nuts_classic(const Model& model, BaseRNG& rng):
        base_hmc<Model, Hamiltonian, Integrator, BaseRNG>(model, rng),
        depth_(0), max_depth_(5), max_delta_(1000),
        n_leapfrog_(0), divergent_(0), energy_(0) {
      }

      ~base_nuts_classic() {}

      void set_max_depth(int d) {
        if (d > 0)
          max_depth_ = d;
      }

      void set_max_delta(double d) {
        max_delta_ = d;
      }

      int get_max_depth() { return this->max_depth_; }
      double get_max_delta() { return this->max_delta_; }

      sample
      transition(sample& init_sample,
                 interface_callbacks::writer::base_writer& info_writer,
                 interface_callbacks::writer::base_writer& error_writer) {
        // Initialize the algorithm
        this->sample_stepsize();

        nuts_util util;

        this->seed(init_sample.cont_params());

        this->hamiltonian_.sample_p(this->z_, this->rand_int_);
        this->hamiltonian_.init(this->z_, info_writer, error_writer);

        ps_point z_plus(this->z_);
        ps_point z_minus(z_plus);

        ps_point z_sample(z_plus);
        ps_point z_propose(z_plus);

        int n_cont = init_sample.cont_params().size();

        Eigen::VectorXd rho_init = this->z_.p;
        Eigen::VectorXd rho_plus(n_cont); rho_plus.setZero();
        Eigen::VectorXd rho_minus(n_cont); rho_minus.setZero();

        util.H0 = this->hamiltonian_.H(this->z_);

        // Sample the slice variable
        util.log_u = std::log(this->rand_uniform_());

        // Build a balanced binary tree until the NUTS criterion fails
        util.criterion = true;
        int n_valid = 0;

        this->depth_ = 0;
        this->divergent_ = 0;

        util.n_tree = 0;
        util.sum_prob = 0;

        while (util.criterion && (this->depth_ <= this->max_depth_)) {
          // Randomly sample a direction in time
          ps_point* z = 0;
          Eigen::VectorXd* rho = 0;

          if (this->rand_uniform_() > 0.5) {
            z = &z_plus;
            rho = &rho_plus;
            util.sign = 1;
          } else {
            z = &z_minus;
            rho = &rho_minus;
            util.sign = -1;
          }

          // And build a new subtree in that direction
          this->z_.ps_point::operator=(*z);

          int n_valid_subtree = build_tree(depth_, *rho, 0, z_propose, util,
                                           info_writer, error_writer);
          ++(this->depth_);

          *z = this->z_;

          // Metropolis-Hastings sample the fresh subtree
          if (!util.criterion)
            break;

          double subtree_prob = 0;

          if (n_valid) {
            subtree_prob = static_cast<double>(n_valid_subtree) /
              static_cast<double>(n_valid);
          } else {
            subtree_prob = n_valid_subtree ? 1 : 0;
          }

          if (this->rand_uniform_() < subtree_prob)
            z_sample = z_propose;

          n_valid += n_valid_subtree;

          // Check validity of completed tree
          this->z_.ps_point::operator=(z_plus);
          Eigen::VectorXd delta_rho = rho_minus + rho_init + rho_plus;

          util.criterion = compute_criterion(z_minus, this->z_, delta_rho);
        }

        this->n_leapfrog_ = util.n_tree;

        double accept_prob = util.sum_prob / static_cast<double>(util.n_tree);

        this->z_.ps_point::operator=(z_sample);
        this->energy_ = this->hamiltonian_.H(this->z_);
        return sample(this->z_.q, - this->z_.V, accept_prob);
      }

      void get_sampler_param_names(std::vector<std::string>& names) {
        names.push_back("stepsize__");
        names.push_back("treedepth__");
        names.push_back("n_leapfrog__");
        names.push_back("divergent__");
        names.push_back("energy__");
      }

      void get_sampler_params(std::vector<double>& values) {
        values.push_back(this->epsilon_);
        values.push_back(this->depth_);
        values.push_back(this->n_leapfrog_);
        values.push_back(this->divergent_);
        values.push_back(this->energy_);
      }

      virtual bool compute_criterion(ps_point& start,
                                     typename Hamiltonian<Model, BaseRNG>
                                     ::PointType& finish,
                                     Eigen::VectorXd& rho) = 0;

      // Returns number of valid points in the completed subtree
      int build_tree(int depth, Eigen::VectorXd& rho,
                     ps_point* z_init_parent, ps_point& z_propose,
                     nuts_util& util,
                     interface_callbacks::writer::base_writer& info_writer,
                     interface_callbacks::writer::base_writer& error_writer) {
        // Base case
        if (depth == 0) {
            this->integrator_.evolve(this->z_, this->hamiltonian_,
                                     util.sign * this->epsilon_,
                                     info_writer, error_writer);
            rho += this->z_.p;

            if (z_init_parent) *z_init_parent = this->z_;
            z_propose = this->z_;

            double h = this->hamiltonian_.H(this->z_);
            if (boost::math::isnan(h))
              h = std::numeric_limits<double>::infinity();

            util.criterion = util.log_u + (h - util.H0) < this->max_delta_;
            if (!util.criterion) ++(this->divergent_);

            util.sum_prob += std::min(1.0, std::exp(util.H0 - h));
            util.n_tree += 1;

            return (util.log_u + (h - util.H0) < 0);

          } else {
          // General recursion
          Eigen::VectorXd left_subtree_rho(rho.size());
          left_subtree_rho.setZero();
          ps_point z_init(this->z_);

          int n1 = build_tree(depth - 1, left_subtree_rho, &z_init,
                              z_propose, util,
                              info_writer, error_writer);

          if (z_init_parent) *z_init_parent = z_init;

          if (!util.criterion) return 0;

          Eigen::VectorXd right_subtree_rho(rho.size());
          right_subtree_rho.setZero();
          ps_point z_propose_right(z_init);

          int n2 = build_tree(depth - 1, right_subtree_rho, 0,
                              z_propose_right, util,
                              info_writer, error_writer);

          double accept_prob = static_cast<double>(n2) /
            static_cast<double>(n1 + n2);

          if ( util.criterion && (this->rand_uniform_() < accept_prob) )
            z_propose = z_propose_right;

          Eigen::VectorXd& subtree_rho = left_subtree_rho;
          subtree_rho += right_subtree_rho;

          rho += subtree_rho;

          util.criterion &= compute_criterion(z_init, this->z_, subtree_rho);

          return n1 + n2;
        }
      }

      int depth_;
      int max_depth_;
      double max_delta_;

      int n_leapfrog_;
      int divergent_;
      double energy_;
    };

  }  // mcmc
}  // stan
#endif
